Question 1

Which of the labeled points below are influential points?

Accepted Answer

A) Points B and D 
B) Point C 
C) Points A,B,and D 
D) Point B 
E) Points A,B,C,and D 
A) Points B and D 
B) Point C 
C) Points A,B,and D 
D) Point B 
E) Points A,B,C,and D

Question 2

The figure below shows the association between life expectancy and infant mortality for several different countries.Also shown is the equation and correlation from a regression analysis.What is the correct conclusion to draw from the figure?

Accepted Answer

A) Countries that have low life expectancies and high infant mortality rates seem to have less regard for the sanctity of human life. 
B) While there appears to be a very strong association,there is probably not a cause-and-effect relationship between infant mortality and life expectancy.Access to basic health care is probably a lurking variable that drives both life expectancy and infant mortality. 
C) Those countries with low life expectancies clearly have no regard for children or expectant mothers. 
D) The association must be coincidental.I would expect the association to have a positive slope,not the negative one illustrated above. 
E) High infant mortality is causing reduced life expectancy,probably because of the increased emotional stress exerted on parents who have lost a child at birth. 
A) Countries that have low life expectancies and high infant mortality rates seem to have less regard for the sanctity of human life. 
B) While there appears to be a very strong association,there is probably not a cause-and-effect relationship between infant mortality and life expectancy.Access to basic health care is probably a lurking variable that drives both life expectancy and infant mortality. 
C) Those countries with low life expectancies clearly have no regard for children or expectant mothers. 
D) The association must be coincidental.I would expect the association to have a positive slope,not the negative one illustrated above. 
E) High infant mortality is causing reduced life expectancy,probably because of the increased emotional stress exerted on parents who have lost a child at birth.

Question 3

The figure below examines the association between life expectancy and computer ownership for several countries.Also shown are the equation and R2 value from a linear regression analysis.What is the best conclusion to draw from the figure?

Accepted Answer

A) Exposure to the radiation from computer monitors is causing a clear decline in life expectancy. 
B) Persons who live longer buy more computers over the course of their longer lifetimes. 
C) Although the association is strong,computer ownership probably does not promote longevity.Instead,national per capita wealth is probably a lurking variable that drives both life expectancy and computer ownership. 
D) Computer ownership promotes health and long life,probably due to the greater access that computer owners have to health information on the world-wide web. 
E) Clearly,there must be some as-yet unknown health benefit associated with using computers. 
A) Exposure to the radiation from computer monitors is causing a clear decline in life expectancy. 
B) Persons who live longer buy more computers over the course of their longer lifetimes. 
C) Although the association is strong,computer ownership probably does not promote longevity.Instead,national per capita wealth is probably a lurking variable that drives both life expectancy and computer ownership. 
D) Computer ownership promotes health and long life,probably due to the greater access that computer owners have to health information on the world-wide web. 
E) Clearly,there must be some as-yet unknown health benefit associated with using computers.

Question 4

The table below displays the latitude (degrees north)and average daily minimum temperature in January (in degrees Fahrenheit)for some cities located in the northern hemisphere. Latitude (Deg North)Average Daily Min Temp in Jan (°F)
Athens,Greece 38 42
Mumbai,India 19 62
Cairo,Egypt 30 47
London,England 51 35
Mexico City,Mexico 19 42
Moscow,Russia 55 9
Paris,France 49 32
Bangkok,Thailand 13 67
Tokyo,Japan 35 29
Manila,Philippines 14 69
The scatter plot and regression equation are shown below:   The regression analysis of this data yields the following values: $$\begin{array} {| l | l |} 
\hline
\text { Variable } & \text { Coefficient } \
\hline \text { Constant } & 76.94 \
\hline \text { Latitude } & 1.038 \
\hline
\end{array}$$ R2 = 0.7660
Use this model to predict the average daily minimum temperature in January for Panama City whose latitude is 9 degrees north.

Accepted Answer

A) 9.3°F 
B) 67.6°F 
C) 86.3°F 
D) 61.5°F 
E) 54.0°F 
A) 9.3°F 
B) 67.6°F 
C) 86.3°F 
D) 61.5°F 
E) 54.0°F

Question 5

Which of the following scatterplots of residuals suggests that a linear model may not be applicable?
 I   
II   
III   
IV

Accepted Answer

A) I 
B) III 
C) IV 
D) II 
E) None of the above 
A) I 
B) III 
C) IV 
D) II 
E) None of the above

Question 6

Which of the labeled points below will exert the largest leverage on a linear model of the data?

Accepted Answer

A) Point A 
B) Point B 
C) Point C 
D) Point D 
E) Point E 
A) Point A 
B) Point B 
C) Point C 
D) Point D 
E) Point E

Question 7

A university studied students' grades and established a strong positive association between the high school average of incoming students and their university GPA.Describe three different possible cause-and-effect relationships that might be present.

Accepted Answer

A) Perhaps higher high school averages cause higher university GPAs,or both could be caused by a lurking variable such as the students' IQ. 
B) There is only one cause-and-effect relationship: higher university GPAs cause higher high school averages. 
C) There is only one cause-and-effect relationship: higher high school averages cause higher university GPAs. 
D) There are only two cause-and-effect relationships: higher high school averages cause higher university GPAs,or higher university GPAs cause higher high school averages. 
E) Perhaps higher high school averages cause higher university GPAs,higher university GPAs cause higher high school averages,or both could be caused by a lurking variable such as the students' high school. 
A) Perhaps higher high school averages cause higher university GPAs,or both could be caused by a lurking variable such as the students' IQ. 
B) There is only one cause-and-effect relationship: higher university GPAs cause higher high school averages. 
C) There is only one cause-and-effect relationship: higher high school averages cause higher university GPAs. 
D) There are only two cause-and-effect relationships: higher high school averages cause higher university GPAs,or higher university GPAs cause higher high school averages. 
E) Perhaps higher high school averages cause higher university GPAs,higher university GPAs cause higher high school averages,or both could be caused by a lurking variable such as the students' high school.

Question 8

Which of the labeled points below are outliers?

Accepted Answer

A) Points A,B,C,and D 
B) Point A 
C) Points A,C,and D 
D) Points A and C 
E) Points C and D 
A) Points A,B,C,and D 
B) Point A 
C) Points A,C,and D 
D) Points A and C 
E) Points C and D

Question 9

The table below shows the gestation (in days)and average longevity (in years)for a number of different mammals: $$\begin{array} { l | c c } 
& \text { Gestation (days) } & \text { Average Longevity (years) } \
\hline \text { Black Bear } & 219 & 18 \
\hline \text { Cat (domestic) } & 63 & 12 \
\hline \text { Monkey (Rhesus) } & 166 & 15 \
\hline \text { Lion } & 100 & 15 \
\hline \text { Horse } & 330 & 20 \
\hline \text { Gorilla } & 258 & 20 \
\hline \text { Gray Squirrel } & 44 & 10
\end{array}$$ The scatter plot and regression equation are shown below:   The regression analysis of this data yields the following values: $$\begin{array} { | l | l | } 
\hline \text { Variable } & \text { Coefficient } \
\hline \text { Constant } & 9.90 \
\hline \text { Gestation } & 0.0345 \
\hline
\end{array}$$ R2 = 0.9048 Use this model to predict the average longevity of an African elephant whose gestation is 660 days.

Accepted Answer

A) 32.7 years 
B) 38.7 years 
C) 41.9 years 
D) 22.8 years 
E) 51.2 years 
A) 32.7 years 
B) 38.7 years 
C) 41.9 years 
D) 22.8 years 
E) 51.2 years

Question 10

Over a period of years,a certain town observed the association between the number of people attending churches and the number of people in the city jail.The results are shown on the figure below.Also shown are the equation and R2 value from a linear regression analysis.What is the best conclusion to draw from the figure?

Accepted Answer

A) Although the association is negatively strong,going to church does not cause people to go to jail.Instead,size of the population in the town is probably a lurking variable that drives both the number of people in jail and the number of people attending church to increase together. 
B) More detainees should go to church to improve their behavior. 
C) Although the association is positively strong,going to church does not cause people to go to jail.Instead,size of the population of the town is probably a lurking variable that drives both the number of people in jail and the number of people attending church to increase together. 
D) More people go to church not to go to jail. 
E) Clearly,there must be some as-yet unknown problems associated with going to church. 
A) Although the association is negatively strong,going to church does not cause people to go to jail.Instead,size of the population in the town is probably a lurking variable that drives both the number of people in jail and the number of people attending church to increase together. 
B) More detainees should go to church to improve their behavior. 
C) Although the association is positively strong,going to church does not cause people to go to jail.Instead,size of the population of the town is probably a lurking variable that drives both the number of people in jail and the number of people attending church to increase together. 
D) More people go to church not to go to jail. 
E) Clearly,there must be some as-yet unknown problems associated with going to church.

Question 11

The total home-game attendance for major-league baseball is the sum of all attendees for all stadiums during the entire season.The home attendance (in millions)for a number of years is shown in the table below. $$\begin{array} { | c | c | } 
\hline \text { Year } & \text { Home Attendance (millions) } \
\hline 1978 & 40.6 \
\hline 1979 & 43.5 \
\hline 1980 & 43.0 \
\hline 1981 & 26.6 \
\hline 1982 & 44.6 \
\hline 1983 & 46.3 \
\hline 1984 & 48.7 \
\hline 1985 & 49.0 \
\hline 1986 & 50.5 \
\hline 1987 & 51.8 \
\hline 1988 & 53.2 \
\hline
\end{array}$$ a)Make a scatterplot showing the trend in home attendance.Describe what you see.   b)Determine the correlation,and comment on its significance.
c)Find the equation of the line of regression.Interpret the slope of the equation.
d)Use your model to predict the home attendance for 1998.How much confidence do you have in this prediction? Explain.
e)Use the internet or other resource to find reasons for any outliers you observe in the scatterplot.

Accepted Answer

a) @#IMG-DLM& The data show a strong association w

Question 12

Which of the labeled points below will exert the largest leverage on a linear model of the data?

Accepted Answer

A) Point A 
B) Point B 
C) Point C 
D) Point D 
E) Point E 
A) Point A 
B) Point B 
C) Point C 
D) Point D 
E) Point E

Which of the labeled points below are influential points?

The figure below shows the association between life expectancy and infant mortality for several different countries.Also shown is the equation and correlation from a regression analysis.What is the correct conclusion to draw from the figure?

The figure below examines the association between life expectancy and computer ownership for several countries.Also shown are the equation and R2 value from a linear regression analysis.What is the best conclusion to draw from the figure?

Which of the following scatterplots of residuals suggests that a linear model may not be applicable? I II III IV

Which of the labeled points below will exert the largest leverage on a linear model of the data?

A university studied students' grades and established a strong positive association between the high school average of incoming students and their university GPA.Describe three different possible cause-and-effect relationships that might be present.

Which of the labeled points below are outliers?

Which of the labeled points below will exert the largest leverage on a linear model of the data?

Stats Starts Here

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Understanding Randomness

Sample Surveys

Experiments and Observational Studies

From Randomness to Probability

Probability Rules

Random Variables

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

The Bootstrap

Filters

Exam 8: Regression Wisdom

Which of the labeled points below are influential points?

The figure below shows the association between life expectancy and infant mortality for several different countries.Also shown is the equation and correlation from a regression analysis.What is the correct conclusion to draw from the figure?

The figure below examines the association between life expectancy and computer ownership for several countries.Also shown are the equation and R2 value from a linear regression analysis.What is the best conclusion to draw from the figure?

Which of the following scatterplots of residuals suggests that a linear model may not be applicable? I II III IV

Which of the labeled points below will exert the largest leverage on a linear model of the data?

A university studied students' grades and established a strong positive association between the high school average of incoming students and their university GPA.Describe three different possible cause-and-effect relationships that might be present.

Which of the labeled points below are outliers?

Which of the labeled points below will exert the largest leverage on a linear model of the data?

Stats Starts Here

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Understanding Randomness

Sample Surveys

Experiments and Observational Studies

From Randomness to Probability

Probability Rules

Random Variables

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

The Bootstrap

Filters